https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Brownda&feedformat=atomUW-Math Wiki - User contributions [en]2024-03-28T22:27:01ZUser contributionsMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php?title=NTS/Abstracts&diff=2022NTS/Abstracts2011-05-31T22:33:49Z<p>Brownda: /* Organizer contact information */</p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:]<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts&diff=2021NTS/Abstracts2011-05-31T22:32:49Z<p>Brownda: /* Organizer contact information */</p>
<hr />
<div>== Organizer contact information ==<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:]<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts&diff=2020NTS/Abstracts2011-05-31T22:32:32Z<p>Brownda: Replacing page with '
== Organizer contact information ==
[http://www.math.wisc.edu/~brownda/ David Brown:]
[http://www.math.wisc.edu/~cais/ Bryden Cais:]
<br>
----
Return to the [[NTS|Number...'</p>
<hr />
<div><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts&diff=2019NTS/Abstracts2011-05-31T22:32:08Z<p>Brownda: </p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Let A be an abelian variety over a number field E, and let v be a finite place of E where A has bad, split, semi-stable reduction. Then the toric part of the reduction of A at v gives rise to a partial integral structure on the (l-adic, p-adic, deRham, log crystalline) cohomology group H^1(A_{E_v} ), arising essentially from the character group of the torus. Let η be a Hodge cycle on A; then one can ask if η is rational (in a precise sense) with respect to this new integral structure on the cohomology. This question was first considered by Andre ́.<br />
Using the theory of Shimura varieties and the Faltings-Chai toroidal compactifications of the moduli of principally polarized abelian varieties, we convert this question into one of deciding if a certain sub-scheme of a torus embedding is again a torus embedding. In the situation where the Mumford-Tate group of A has a reductive model over Zp, for v|p (this is the unramified situation), we employ a generalization of the methods introduced by Faltings and Kisin–initially used to construct smooth integral models of Shimura varieties–to answer this question positively.<br />
A by-product of this rationality result is the construction of good toroidal compactifications of the integral models of Shimura varieties mentioned above. This was in fact the main motivation for considering, in the first place, the possibility of such a result. A formal consequence of the existence of these compactifications is the following result, which is a slightly weakened version of a conjecture of Yasuo Morita: Suppose the Mumford-Tate group G of A is anisotropic mod center, then, for any prime p such that G admits a reductive model over Zp, A has potentially good reduction at all finite places v|p of E.<br />
The first part of the talk will be expository: we will introduce Hodge cycles on abelian varieties and their properties, so that we can state the problem at hand. Then, we will switch track and talk about the question on toric embeddings referenced above. After this, we will focus on the case where the reduction of A at v is a split torus. In this case, the theory is more combinatorial, but the key ideas for the general case are already visible. We will quickly sketch the properties that we need of Shimura varieties and the Faltings-Chai compactification, and see how they can be used to reduce the problem to the one about toric embeddings. If time remains, we will say something about how to solve this latter problem using the Faltings-Kisin method.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== Tony Várilly-Alvarado ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Wei Ho ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rob Rhoades ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Chris Davis ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: The "local lifting problem" asks: given a G-Galois extension A/k[[t]], where k is algebraically closed of characteristic p, does there exist a G-Galois extension A_R/R[[t]] that reduces to A/k[[t]], where R is a characteristic zero DVR with residue field k? (here a Galois extension is an extension of integrally closed rings that gives a Galois extension on fraction fields.) The Oort conjecture states that the local lifting problem should always have a solution for G cyclic. This is basic Kummer theory when p does not divide |G|, and has been proven when v_p(|G|) = 1 (Oort, Sekiguchi, Suwa) and when v_p(|G|) = 2 (Green, Matignon). We will first motivate the local lifting problem from geometry, and then we will show that it has a solution for a large family of cyclic extensions. This family includes all extensions where v_p(|G|) = 3 and many extensions where v_p(|G|) is arbitrarily high. This is joint work with Stefan Wewers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bianca Viray ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Descent on elliptic surfaces and transcendental Brauer element <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Elements of the Brauer group of a variety X are hard to<br />
compute. Transcendental elements, i.e. those that are not in the<br />
kernel of the natural map Br X --> Br \overline{X}, are notoriously<br />
difficult. Wittenberg and Ieronymou have developed methods to find<br />
explicit representatives of transcendental elements of an elliptic<br />
surface, in the case that the Jacobian fibration has rational<br />
2-torsion. We use ideas from descent to develop techniques for general<br />
elliptic surfaces.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Frank Thorne ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rafe Jones ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Galois theory of iterated quadratic rational functions <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
<br />
Abstract: I'll describe recent work investigating the arboreal Galoisrepresentation attached to a degree-2 rational function, focusing on the case where the function commuteswith a non-trivial Mobius transformation. In a sense this is a dynamical systems analogue to the p-adic Galois representation attached to an elliptic curve, with particular attention to the CM case. In joint work with Michelle Manes, we give criteria for the image of this representation to be large, and show thatthese criteria are often satisfied in the "CM" case.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jonathan Blackhurst ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Polynomials of the Bifurcation Points of the Logistic Map <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: The logistic map f(r,x)=rx(1-x) was originally studied by ecologists modeling the population of a species from one generation to the next. Here, the population of the next generation f(r,x) depends on the population x of the current generation and a parameter r called the probiotic potential. To find the long-term behavior of the population for a fixed r, we look at iterates of the critical point c=1/2 under the map f. If 0<r<2 the iterates approach zero, so the population goes extinct. If 2<r<3, the iterates approach a single non-zero value, and the population is in equilibrium. If 3<r<1+sqrt(6), the iterates oscillate between two values (even iterates approach one value, while odd iterates approach another) in a boom-and-bust cycle. As r increases, the population begins oscillating between four values, then eight, then sixteen, and this period-doubling continues until an accumulation point (r=3.57, approximately) where the behavior of the population is no longer periodic. Even after the accumulation point, iterates of the critical point may begin again to exhibit periodic behavior. For example, at r=1+sqrt(8), they oscillate between three values. These values of r—2, 3, 1+sqrt(6), and 1+sqrt(8)—where qualitative behavior of the model changes are called bifurcation points. Little has been known about the polynomials these algebraic numbers satisfy. We find their degrees, show that their roots come in pairs whose mean is 1, put constraints on the size and prime factors of their constant coefficients, and record the number of real roots.<br />
|} <br />
</center><br />
<br />
== Liang Xiao ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Computing log-characteristic cycles using ramification theory<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: There is an analogy among vector bundles with integrable<br />
connections, overconvergent F-isocrystals, and lisse l-adic sheaves.<br />
Given one of the objects, the property of being clean says that the<br />
ramification is controlled by the ramification along all generic<br />
points of the ramified divisors. In this case, one expects that the<br />
Euler characteristics may be expressed in terms of (subsidiary) Swan<br />
conductors; and (in first two cases) the log-characteristic cycles may<br />
be described in terms of refined Swan conductors. I will explain the<br />
proof of this in the vector bundle case and report on the recent<br />
progress on the overconvergent F-isocrystal case if time is permitted.<br />
|} <br />
</center><br />
<br />
== Winnie Li ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Modularity of Low Degree Scholl Representations<br />
|-<br />
| bgcolor="#DDDDDD"| To the space of d-dimensional cusp forms of weight k > 2 for<br />
a noncongruence<br />
subgroup of SL(2, Z), Scholl has attached a family of 2d-dimensional<br />
compatible l-adic<br />
representations of the Galois group over Q. Since his construction is<br />
motivic, the associated<br />
L-functions of these representations are expected to agree with<br />
certain automorphic L-functions<br />
according to Langlands' philosophy. In this talk we shall survey<br />
recent progress on this topic.<br />
More precisely, we'll see that this is indeed the case when d=1. This<br />
also holds true when d=2,<br />
provided that the representation space admits quaternion<br />
multiplications. This is a joint work<br />
with Atkin, Liu and Long.<br />
<br />
|} <br />
</center><br />
<br />
<br />
<br />
== Avraham Eizenbud ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Multiplicity One Theorems - a Uniform Proof <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
<br />
Abstract: Let F be a local field of characteristic 0. <br />
We consider distributions on GL(n+1,F) which are invariant under the adjoint action of<br />
GL(n,F). We prove that such distributions are invariant under<br />
transposition. This implies that an irreducible representation of<br />
GL(n+1,F), when restricted to GL(n,F) "decomposes" with multiplicity one.<br />
<br />
<br />
<br />
Such property of a group and a subgroup is called strong Gelfand property.<br />
It is used in representation theory and automorphic forms. This property<br />
was introduced by Gelfand in the 50s for compact groups. However, for <br />
non-compact groups it is much more difficult to establish.<br />
<br />
For our pair (GL(n+1,F),GL(n,F)) it was proven in 2007 in [AGRS] for<br />
non-Archimedean F, and in 2008 in [AG] and [SZ] for Archimedean F. In this<br />
lecture we will present a uniform for both cases. <br />
This proof is based on the above papers and an additional new tool. If time<br />
permits we will discuss similar theorems that hold for orthogonal and<br />
unitary groups.<br />
<br />
[AG] A. Aizenbud, D. Gourevitch, Multiplicity one theorem for (GL(n+1,R),GL(n,R))", arXiv:0808.2729v1 [math.RT]<br />
<br />
[AGRS] A. Aizenbud, D. Gourevitch, S. Rallis, G. Schiffmann, Multiplicity One Theorems, arXiv:0709.4215v1 [math.RT], to appear in the Annals of Mathematics.<br />
<br />
<br />
[SZ] B. Sun and C.-B. Zhu, Multiplicity one theorems: the Archimedean case, preprint available at http://www.math.nus.edu.sg/~matzhucb/Multiplicity_One.pdf<br />
<br />
|} <br />
</center><br />
<br />
<br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts&diff=2018NTS/Abstracts2011-05-31T22:31:45Z<p>Brownda: NTS/Abstracts moved to NTS/Abstracts Spring 2011</p>
<hr />
<div>#REDIRECT [[NTS/Abstracts Spring 2011]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=2017NTS/Abstracts Spring 20112011-05-31T22:31:45Z<p>Brownda: NTS/Abstracts moved to NTS/Abstracts Spring 2011</p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Let A be an abelian variety over a number field E, and let v be a finite place of E where A has bad, split, semi-stable reduction. Then the toric part of the reduction of A at v gives rise to a partial integral structure on the (l-adic, p-adic, deRham, log crystalline) cohomology group H^1(A_{E_v} ), arising essentially from the character group of the torus. Let η be a Hodge cycle on A; then one can ask if η is rational (in a precise sense) with respect to this new integral structure on the cohomology. This question was first considered by Andre ́.<br />
Using the theory of Shimura varieties and the Faltings-Chai toroidal compactifications of the moduli of principally polarized abelian varieties, we convert this question into one of deciding if a certain sub-scheme of a torus embedding is again a torus embedding. In the situation where the Mumford-Tate group of A has a reductive model over Zp, for v|p (this is the unramified situation), we employ a generalization of the methods introduced by Faltings and Kisin–initially used to construct smooth integral models of Shimura varieties–to answer this question positively.<br />
A by-product of this rationality result is the construction of good toroidal compactifications of the integral models of Shimura varieties mentioned above. This was in fact the main motivation for considering, in the first place, the possibility of such a result. A formal consequence of the existence of these compactifications is the following result, which is a slightly weakened version of a conjecture of Yasuo Morita: Suppose the Mumford-Tate group G of A is anisotropic mod center, then, for any prime p such that G admits a reductive model over Zp, A has potentially good reduction at all finite places v|p of E.<br />
The first part of the talk will be expository: we will introduce Hodge cycles on abelian varieties and their properties, so that we can state the problem at hand. Then, we will switch track and talk about the question on toric embeddings referenced above. After this, we will focus on the case where the reduction of A at v is a split torus. In this case, the theory is more combinatorial, but the key ideas for the general case are already visible. We will quickly sketch the properties that we need of Shimura varieties and the Faltings-Chai compactification, and see how they can be used to reduce the problem to the one about toric embeddings. If time remains, we will say something about how to solve this latter problem using the Faltings-Kisin method.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== Tony Várilly-Alvarado ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Wei Ho ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rob Rhoades ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Chris Davis ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: The "local lifting problem" asks: given a G-Galois extension A/k[[t]], where k is algebraically closed of characteristic p, does there exist a G-Galois extension A_R/R[[t]] that reduces to A/k[[t]], where R is a characteristic zero DVR with residue field k? (here a Galois extension is an extension of integrally closed rings that gives a Galois extension on fraction fields.) The Oort conjecture states that the local lifting problem should always have a solution for G cyclic. This is basic Kummer theory when p does not divide |G|, and has been proven when v_p(|G|) = 1 (Oort, Sekiguchi, Suwa) and when v_p(|G|) = 2 (Green, Matignon). We will first motivate the local lifting problem from geometry, and then we will show that it has a solution for a large family of cyclic extensions. This family includes all extensions where v_p(|G|) = 3 and many extensions where v_p(|G|) is arbitrarily high. This is joint work with Stefan Wewers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bianca Viray ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Descent on elliptic surfaces and transcendental Brauer element <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Elements of the Brauer group of a variety X are hard to<br />
compute. Transcendental elements, i.e. those that are not in the<br />
kernel of the natural map Br X --> Br \overline{X}, are notoriously<br />
difficult. Wittenberg and Ieronymou have developed methods to find<br />
explicit representatives of transcendental elements of an elliptic<br />
surface, in the case that the Jacobian fibration has rational<br />
2-torsion. We use ideas from descent to develop techniques for general<br />
elliptic surfaces.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Frank Thorne ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rafe Jones ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Galois theory of iterated quadratic rational functions <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
<br />
Abstract: I'll describe recent work investigating the arboreal Galoisrepresentation attached to a degree-2 rational function, focusing on the case where the function commuteswith a non-trivial Mobius transformation. In a sense this is a dynamical systems analogue to the p-adic Galois representation attached to an elliptic curve, with particular attention to the CM case. In joint work with Michelle Manes, we give criteria for the image of this representation to be large, and show thatthese criteria are often satisfied in the "CM" case.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jonathan Blackhurst ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Polynomials of the Bifurcation Points of the Logistic Map <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: The logistic map f(r,x)=rx(1-x) was originally studied by ecologists modeling the population of a species from one generation to the next. Here, the population of the next generation f(r,x) depends on the population x of the current generation and a parameter r called the probiotic potential. To find the long-term behavior of the population for a fixed r, we look at iterates of the critical point c=1/2 under the map f. If 0<r<2 the iterates approach zero, so the population goes extinct. If 2<r<3, the iterates approach a single non-zero value, and the population is in equilibrium. If 3<r<1+sqrt(6), the iterates oscillate between two values (even iterates approach one value, while odd iterates approach another) in a boom-and-bust cycle. As r increases, the population begins oscillating between four values, then eight, then sixteen, and this period-doubling continues until an accumulation point (r=3.57, approximately) where the behavior of the population is no longer periodic. Even after the accumulation point, iterates of the critical point may begin again to exhibit periodic behavior. For example, at r=1+sqrt(8), they oscillate between three values. These values of r—2, 3, 1+sqrt(6), and 1+sqrt(8)—where qualitative behavior of the model changes are called bifurcation points. Little has been known about the polynomials these algebraic numbers satisfy. We find their degrees, show that their roots come in pairs whose mean is 1, put constraints on the size and prime factors of their constant coefficients, and record the number of real roots.<br />
|} <br />
</center><br />
<br />
== Liang Xiao ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Computing log-characteristic cycles using ramification theory<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: There is an analogy among vector bundles with integrable<br />
connections, overconvergent F-isocrystals, and lisse l-adic sheaves.<br />
Given one of the objects, the property of being clean says that the<br />
ramification is controlled by the ramification along all generic<br />
points of the ramified divisors. In this case, one expects that the<br />
Euler characteristics may be expressed in terms of (subsidiary) Swan<br />
conductors; and (in first two cases) the log-characteristic cycles may<br />
be described in terms of refined Swan conductors. I will explain the<br />
proof of this in the vector bundle case and report on the recent<br />
progress on the overconvergent F-isocrystal case if time is permitted.<br />
|} <br />
</center><br />
<br />
== Winnie Li ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Modularity of Low Degree Scholl Representations<br />
|-<br />
| bgcolor="#DDDDDD"| To the space of d-dimensional cusp forms of weight k > 2 for<br />
a noncongruence<br />
subgroup of SL(2, Z), Scholl has attached a family of 2d-dimensional<br />
compatible l-adic<br />
representations of the Galois group over Q. Since his construction is<br />
motivic, the associated<br />
L-functions of these representations are expected to agree with<br />
certain automorphic L-functions<br />
according to Langlands' philosophy. In this talk we shall survey<br />
recent progress on this topic.<br />
More precisely, we'll see that this is indeed the case when d=1. This<br />
also holds true when d=2,<br />
provided that the representation space admits quaternion<br />
multiplications. This is a joint work<br />
with Atkin, Liu and Long.<br />
<br />
|} <br />
</center><br />
<br />
<br />
<br />
== Avraham Eizenbud ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Multiplicity One Theorems - a Uniform Proof <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
<br />
Abstract: Let F be a local field of characteristic 0. <br />
We consider distributions on GL(n+1,F) which are invariant under the adjoint action of<br />
GL(n,F). We prove that such distributions are invariant under<br />
transposition. This implies that an irreducible representation of<br />
GL(n+1,F), when restricted to GL(n,F) "decomposes" with multiplicity one.<br />
<br />
<br />
<br />
Such property of a group and a subgroup is called strong Gelfand property.<br />
It is used in representation theory and automorphic forms. This property<br />
was introduced by Gelfand in the 50s for compact groups. However, for <br />
non-compact groups it is much more difficult to establish.<br />
<br />
For our pair (GL(n+1,F),GL(n,F)) it was proven in 2007 in [AGRS] for<br />
non-Archimedean F, and in 2008 in [AG] and [SZ] for Archimedean F. In this<br />
lecture we will present a uniform for both cases. <br />
This proof is based on the above papers and an additional new tool. If time<br />
permits we will discuss similar theorems that hold for orthogonal and<br />
unitary groups.<br />
<br />
[AG] A. Aizenbud, D. Gourevitch, Multiplicity one theorem for (GL(n+1,R),GL(n,R))", arXiv:0808.2729v1 [math.RT]<br />
<br />
[AGRS] A. Aizenbud, D. Gourevitch, S. Rallis, G. Schiffmann, Multiplicity One Theorems, arXiv:0709.4215v1 [math.RT], to appear in the Annals of Mathematics.<br />
<br />
<br />
[SZ] B. Sun and C.-B. Zhu, Multiplicity one theorems: the Archimedean case, preprint available at http://www.math.nus.edu.sg/~matzhucb/Multiplicity_One.pdf<br />
<br />
|} <br />
</center><br />
<br />
<br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_Fall_2011&diff=2016NTS Fall 20112011-05-31T22:30:38Z<p>Brownda: /* Fall 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm.<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Fall 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 1 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (Caltech)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Solution to RH</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 8 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (Caltech)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Solution to RH</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 15 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (Caltech)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Solution to RH</em></font>]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:]<br />
<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Spring 2011 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_Fall_2011&diff=2015NTS Fall 20112011-05-31T22:30:22Z<p>Brownda: /* Fall 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm.<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Fall 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 1 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (Caltech)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Solution to RH</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 8 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (Caltech)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Solution to RH</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 15 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (Caltech)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Solution to RH</em></font>]]<br />
|}<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:]<br />
<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Spring 2011 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_Fall_2011&diff=2014NTS Fall 20112011-05-31T22:30:12Z<p>Brownda: /* Fall 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm.<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Fall 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 1 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (Caltech)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Solution to RH</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 8 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (Caltech)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Solution to RH</em></font>]]<br />
|}<br />
|-<br />
| bgcolor="#E0E0E0"| September 15 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (Caltech)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Solution to RH</em></font>]]<br />
|}<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:]<br />
<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Spring 2011 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_Fall_2011&diff=2013NTS Fall 20112011-05-31T22:29:44Z<p>Brownda: /* Fall 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm.<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Fall 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 1 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (Caltech)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Solution to RH</em></font>]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:]<br />
<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Spring 2011 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_Fall_2011&diff=2012NTS Fall 20112011-05-31T22:27:54Z<p>Brownda: </p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm.<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Fall 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#David_Brown | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Tony_Várilly-Alvarado | <font color="black"><em>Failure of the Hasse principle for Enriques surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| Shamgar Gurevich<br> UW-Madison <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em> Fast Fourier Transform: Why? and How? </em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>Descent on elliptic surfaces and transcendental Brauer element</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bhargav Bhatt <br> (University of Michigan) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bharvav_Bhatt | <font color="black"><em>Integral structures on de Rham<br />
cohomology</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>Galois theory of iterated quadratic rational functions</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>Modularity of Low Degree Scholl Representations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 5 (Thurs)<br />
| bgcolor="#F0B0B0"| Rami Aizenbud, <br> MIT<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em> Multiplicity One Theorems - a Uniform Proof </em></font>]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:]<br />
<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Spring 2011 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_Fall_2011&diff=2011NTS Fall 20112011-05-31T22:26:38Z<p>Brownda: New page: = Number Theory Seminar, University of Wisconsin-Madison = *'''When:''' Thursdays at 2:30pm. *'''Where:''' Van Vleck Hall B129 *Please join the [https://mailhost.math.wisc.edu/mailman/l...</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm.<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Fall 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#David_Brown | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Tony_Várilly-Alvarado | <font color="black"><em>Failure of the Hasse principle for Enriques surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| Shamgar Gurevich<br> UW-Madison <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em> Fast Fourier Transform: Why? and How? </em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>Descent on elliptic surfaces and transcendental Brauer element</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bhargav Bhatt <br> (University of Michigan) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bharvav_Bhatt | <font color="black"><em>Integral structures on de Rham<br />
cohomology</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>Galois theory of iterated quadratic rational functions</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>Modularity of Low Degree Scholl Representations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 5 (Thurs)<br />
| bgcolor="#F0B0B0"| Rami Aizenbud, <br> MIT<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em> Multiplicity One Theorems - a Uniform Proof </em></font>]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS&diff=2010NTS2011-05-31T22:25:50Z<p>Brownda: Redirecting to NTS Fall 2011</p>
<hr />
<div>#REDIRECT [[NTS Fall 2011]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1911NTS spring 20112011-04-09T23:24:18Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#David_Brown | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Tony_Várilly-Alvarado | <font color="black"><em>Failure of the Hasse principle for Enriques surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| Shamgar Gurevich<br> UW-Madison <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em> Fast Fourier Transform: Why? and How? </em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>Descent on elliptic surfaces and transcendental Brauer element</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bhargav Bhatt <br> (University of Michigan) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bharvav_Bhatt | <font color="black"><em>Integral structures on de Rham<br />
cohomology</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>Galois theory of iterated quadratic rational functions</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 5 (Thurs)<br />
| bgcolor="#F0B0B0"| Rami Aizenbud, <br> MIT<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em> Multiplicity One Theorems </em></font>]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1895NTS/Abstracts Spring 20112011-03-30T23:02:33Z<p>Brownda: /* Bianca Viray */</p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Let A be an abelian variety over a number field E, and let v be a finite place of E where A has bad, split, semi-stable reduction. Then the toric part of the reduction of A at v gives rise to a partial integral structure on the (l-adic, p-adic, deRham, log crystalline) cohomology group H^1(A_{E_v} ), arising essentially from the character group of the torus. Let η be a Hodge cycle on A; then one can ask if η is rational (in a precise sense) with respect to this new integral structure on the cohomology. This question was first considered by Andre ́.<br />
Using the theory of Shimura varieties and the Faltings-Chai toroidal compactifications of the moduli of principally polarized abelian varieties, we convert this question into one of deciding if a certain sub-scheme of a torus embedding is again a torus embedding. In the situation where the Mumford-Tate group of A has a reductive model over Zp, for v|p (this is the unramified situation), we employ a generalization of the methods introduced by Faltings and Kisin–initially used to construct smooth integral models of Shimura varieties–to answer this question positively.<br />
A by-product of this rationality result is the construction of good toroidal compactifications of the integral models of Shimura varieties mentioned above. This was in fact the main motivation for considering, in the first place, the possibility of such a result. A formal consequence of the existence of these compactifications is the following result, which is a slightly weakened version of a conjecture of Yasuo Morita: Suppose the Mumford-Tate group G of A is anisotropic mod center, then, for any prime p such that G admits a reductive model over Zp, A has potentially good reduction at all finite places v|p of E.<br />
The first part of the talk will be expository: we will introduce Hodge cycles on abelian varieties and their properties, so that we can state the problem at hand. Then, we will switch track and talk about the question on toric embeddings referenced above. After this, we will focus on the case where the reduction of A at v is a split torus. In this case, the theory is more combinatorial, but the key ideas for the general case are already visible. We will quickly sketch the properties that we need of Shimura varieties and the Faltings-Chai compactification, and see how they can be used to reduce the problem to the one about toric embeddings. If time remains, we will say something about how to solve this latter problem using the Faltings-Kisin method.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== Tony Várilly-Alvarado ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Wei Ho ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rob Rhoades ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Chris Davis ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: The "local lifting problem" asks: given a G-Galois extension A/k[[t]], where k is algebraically closed of characteristic p, does there exist a G-Galois extension A_R/R[[t]] that reduces to A/k[[t]], where R is a characteristic zero DVR with residue field k? (here a Galois extension is an extension of integrally closed rings that gives a Galois extension on fraction fields.) The Oort conjecture states that the local lifting problem should always have a solution for G cyclic. This is basic Kummer theory when p does not divide |G|, and has been proven when v_p(|G|) = 1 (Oort, Sekiguchi, Suwa) and when v_p(|G|) = 2 (Green, Matignon). We will first motivate the local lifting problem from geometry, and then we will show that it has a solution for a large family of cyclic extensions. This family includes all extensions where v_p(|G|) = 3 and many extensions where v_p(|G|) is arbitrarily high. This is joint work with Stefan Wewers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bianca Viray ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Descent on elliptic surfaces and transcendental Brauer element <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Elements of the Brauer group of a variety X are hard to<br />
compute. Transcendental elements, i.e. those that are not in the<br />
kernel of the natural map Br X --> Br \overline{X}, are notoriously<br />
difficult. Wittenberg and Ieronymou have developed methods to find<br />
explicit representatives of transcendental elements of an elliptic<br />
surface, in the case that the Jacobian fibration has rational<br />
2-torsion. We use ideas from descent to develop techniques for general<br />
elliptic surfaces.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Frank Thorne ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rafe Jones ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Galois theory of iterated quadratic rational functions <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
<br />
Abstract: I'll describe recent work investigating the arboreal Galoisrepresentation attached to a degree-2 rational function, focusing on the case where the function commuteswith a non-trivial Mobius transformation. In a sense this is a dynamical systems analogue to the p-adic Galois representation attached to an elliptic curve, with particular attention to the CM case. In joint work with Michelle Manes, we give criteria for the image of this representation to be large, and show thatthese criteria are often satisfied in the "CM" case.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jonathan Blackhurst ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Polynomials of the Bifurcation Points of the Logistic Map <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: The logistic map f(r,x)=rx(1-x) was originally studied by ecologists modeling the population of a species from one generation to the next. Here, the population of the next generation f(r,x) depends on the population x of the current generation and a parameter r called the probiotic potential. To find the long-term behavior of the population for a fixed r, we look at iterates of the critical point c=1/2 under the map f. If 0<r<2 the iterates approach zero, so the population goes extinct. If 2<r<3, the iterates approach a single non-zero value, and the population is in equilibrium. If 3<r<1+sqrt(6), the iterates oscillate between two values (even iterates approach one value, while odd iterates approach another) in a boom-and-bust cycle. As r increases, the population begins oscillating between four values, then eight, then sixteen, and this period-doubling continues until an accumulation point (r=3.57, approximately) where the behavior of the population is no longer periodic. Even after the accumulation point, iterates of the critical point may begin again to exhibit periodic behavior. For example, at r=1+sqrt(8), they oscillate between three values. These values of r—2, 3, 1+sqrt(6), and 1+sqrt(8)—where qualitative behavior of the model changes are called bifurcation points. Little has been known about the polynomials these algebraic numbers satisfy. We find their degrees, show that their roots come in pairs whose mean is 1, put constraints on the size and prime factors of their constant coefficients, and record the number of real roots.<br />
|} <br />
</center><br />
<br />
== Liang Xiao ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: There is an analogy among vector bundles with integrable<br />
connections, overconvergent F-isocrystals, and lisse l-adic sheaves.<br />
Given one of the objects, the property of being clean says that the<br />
ramification is controlled by the ramification along all generic<br />
points of the ramified divisors. In this case, one expects that the<br />
Euler characteristics may be expressed in terms of (subsidiary) Swan<br />
conductors; and (in first two cases) the log-characteristic cycles may<br />
be described in terms of refined Swan conductors. I will explain the<br />
proof of this in the vector bundle case and report on the recent<br />
progress on the overconvergent F-isocrystal case if time is permitted.<br />
|} <br />
</center><br />
<br />
== Winnie Li ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=1894NTSGrad2011-03-30T22:04:11Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Graduate Student Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Tuesdays at 2:30pm<br />
*'''Where:''' Van Vleck Hall B105 (or possibly B129)<br />
<br />
<br><br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk. <br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 18 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>Organizational meeting</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 25 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Silas Johnson<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>Introduction to Hodge Structures and the Mumford-Tate group</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Mike Woodbury<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Evan Dummit<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>An introduction to Stark's conjecture</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 15 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Daniel Ross<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 22 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Lalit Jain <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 1 (Tue.)<br />
| bgcolor="#F0B0B0"|<br> Luanlei Zhao<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Intro to Jacob forms</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 8 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Marton Hablicsek<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 15 (Tue.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em></em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 22 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Yueke Hu<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 29 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Rachel Davis<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 5 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Timur Nezhmetdinov<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 12 (Tue.)<br />
| bgcolor="#F0B0B0"| No Talk<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em></em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 19 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Andrew Bridy<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 26 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Jonathan Blackhurst<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Jonathan_Blackhurst | <font color="black"><em>Polynomials of the Bifurcation Points of the Logistic Map</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
----<br />
The Fall 2010 NTS Grad page has moved [http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2010 here:].<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1884NTS/Abstracts Spring 20112011-03-27T13:35:53Z<p>Brownda: /* Andrew Obus */</p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Let A be an abelian variety over a number field E, and let v be a finite place of E where A has bad, split, semi-stable reduction. Then the toric part of the reduction of A at v gives rise to a partial integral structure on the (l-adic, p-adic, deRham, log crystalline) cohomology group H^1(A_{E_v} ), arising essentially from the character group of the torus. Let η be a Hodge cycle on A; then one can ask if η is rational (in a precise sense) with respect to this new integral structure on the cohomology. This question was first considered by Andre ́.<br />
Using the theory of Shimura varieties and the Faltings-Chai toroidal compactifications of the moduli of principally polarized abelian varieties, we convert this question into one of deciding if a certain sub-scheme of a torus embedding is again a torus embedding. In the situation where the Mumford-Tate group of A has a reductive model over Zp, for v|p (this is the unramified situation), we employ a generalization of the methods introduced by Faltings and Kisin–initially used to construct smooth integral models of Shimura varieties–to answer this question positively.<br />
A by-product of this rationality result is the construction of good toroidal compactifications of the integral models of Shimura varieties mentioned above. This was in fact the main motivation for considering, in the first place, the possibility of such a result. A formal consequence of the existence of these compactifications is the following result, which is a slightly weakened version of a conjecture of Yasuo Morita: Suppose the Mumford-Tate group G of A is anisotropic mod center, then, for any prime p such that G admits a reductive model over Zp, A has potentially good reduction at all finite places v|p of E.<br />
The first part of the talk will be expository: we will introduce Hodge cycles on abelian varieties and their properties, so that we can state the problem at hand. Then, we will switch track and talk about the question on toric embeddings referenced above. After this, we will focus on the case where the reduction of A at v is a split torus. In this case, the theory is more combinatorial, but the key ideas for the general case are already visible. We will quickly sketch the properties that we need of Shimura varieties and the Faltings-Chai compactification, and see how they can be used to reduce the problem to the one about toric embeddings. If time remains, we will say something about how to solve this latter problem using the Faltings-Kisin method.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== Tony Várilly-Alvarado ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Wei Ho ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rob Rhoades ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Chris Davis ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: The "local lifting problem" asks: given a G-Galois extension A/k[[t]], where k is algebraically closed of characteristic p, does there exist a G-Galois extension A_R/R[[t]] that reduces to A/k[[t]], where R is a characteristic zero DVR with residue field k? (here a Galois extension is an extension of integrally closed rings that gives a Galois extension on fraction fields.) The Oort conjecture states that the local lifting problem should always have a solution for G cyclic. This is basic Kummer theory when p does not divide |G|, and has been proven when v_p(|G|) = 1 (Oort, Sekiguchi, Suwa) and when v_p(|G|) = 2 (Green, Matignon). We will first motivate the local lifting problem from geometry, and then we will show that it has a solution for a large family of cyclic extensions. This family includes all extensions where v_p(|G|) = 3 and many extensions where v_p(|G|) is arbitrarily high. This is joint work with Stefan Wewers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bianca Viray ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Frank Thorne ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rafe Jones ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Galois theory of iterated quadratic rational functions <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
<br />
Abstract: I'll describe recent work investigating the arboreal Galoisrepresentation attached to a degree-2 rational function, focusing on the case where the function commuteswith a non-trivial Mobius transformation. In a sense this is a dynamical systems analogue to the p-adic Galois representation attached to an elliptic curve, with particular attention to the CM case. In joint work with Michelle Manes, we give criteria for the image of this representation to be large, and show thatthese criteria are often satisfied in the "CM" case.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jonathan Blackhurst ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Polynomials of the Bifurcation Points of the Logistic Map <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: The logistic map f(r,x)=rx(1-x) was originally studied by ecologists modeling the population of a species from one generation to the next. Here, the population of the next generation f(r,x) depends on the population x of the current generation and a parameter r called the probiotic potential. To find the long-term behavior of the population for a fixed r, we look at iterates of the critical point c=1/2 under the map f. If 0<r<2 the iterates approach zero, so the population goes extinct. If 2<r<3, the iterates approach a single non-zero value, and the population is in equilibrium. If 3<r<1+sqrt(6), the iterates oscillate between two values (even iterates approach one value, while odd iterates approach another) in a boom-and-bust cycle. As r increases, the population begins oscillating between four values, then eight, then sixteen, and this period-doubling continues until an accumulation point (r=3.57, approximately) where the behavior of the population is no longer periodic. Even after the accumulation point, iterates of the critical point may begin again to exhibit periodic behavior. For example, at r=1+sqrt(8), they oscillate between three values. These values of r—2, 3, 1+sqrt(6), and 1+sqrt(8)—where qualitative behavior of the model changes are called bifurcation points. Little has been known about the polynomials these algebraic numbers satisfy. We find their degrees, show that their roots come in pairs whose mean is 1, put constraints on the size and prime factors of their constant coefficients, and record the number of real roots.<br />
|} <br />
</center><br />
<br />
== Liang Xiao ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: There is an analogy among vector bundles with integrable<br />
connections, overconvergent F-isocrystals, and lisse l-adic sheaves.<br />
Given one of the objects, the property of being clean says that the<br />
ramification is controlled by the ramification along all generic<br />
points of the ramified divisors. In this case, one expects that the<br />
Euler characteristics may be expressed in terms of (subsidiary) Swan<br />
conductors; and (in first two cases) the log-characteristic cycles may<br />
be described in terms of refined Swan conductors. I will explain the<br />
proof of this in the vector bundle case and report on the recent<br />
progress on the overconvergent F-isocrystal case if time is permitted.<br />
|} <br />
</center><br />
<br />
== Winnie Li ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1883NTS/Abstracts Spring 20112011-03-25T20:57:13Z<p>Brownda: /* Rafe Jones */</p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Let A be an abelian variety over a number field E, and let v be a finite place of E where A has bad, split, semi-stable reduction. Then the toric part of the reduction of A at v gives rise to a partial integral structure on the (l-adic, p-adic, deRham, log crystalline) cohomology group H^1(A_{E_v} ), arising essentially from the character group of the torus. Let η be a Hodge cycle on A; then one can ask if η is rational (in a precise sense) with respect to this new integral structure on the cohomology. This question was first considered by Andre ́.<br />
Using the theory of Shimura varieties and the Faltings-Chai toroidal compactifications of the moduli of principally polarized abelian varieties, we convert this question into one of deciding if a certain sub-scheme of a torus embedding is again a torus embedding. In the situation where the Mumford-Tate group of A has a reductive model over Zp, for v|p (this is the unramified situation), we employ a generalization of the methods introduced by Faltings and Kisin–initially used to construct smooth integral models of Shimura varieties–to answer this question positively.<br />
A by-product of this rationality result is the construction of good toroidal compactifications of the integral models of Shimura varieties mentioned above. This was in fact the main motivation for considering, in the first place, the possibility of such a result. A formal consequence of the existence of these compactifications is the following result, which is a slightly weakened version of a conjecture of Yasuo Morita: Suppose the Mumford-Tate group G of A is anisotropic mod center, then, for any prime p such that G admits a reductive model over Zp, A has potentially good reduction at all finite places v|p of E.<br />
The first part of the talk will be expository: we will introduce Hodge cycles on abelian varieties and their properties, so that we can state the problem at hand. Then, we will switch track and talk about the question on toric embeddings referenced above. After this, we will focus on the case where the reduction of A at v is a split torus. In this case, the theory is more combinatorial, but the key ideas for the general case are already visible. We will quickly sketch the properties that we need of Shimura varieties and the Faltings-Chai compactification, and see how they can be used to reduce the problem to the one about toric embeddings. If time remains, we will say something about how to solve this latter problem using the Faltings-Kisin method.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== Tony Várilly-Alvarado ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Wei Ho ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rob Rhoades ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Chris Davis ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bianca Viray ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Frank Thorne ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rafe Jones ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Galois theory of iterated quadratic rational functions <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
<br />
Abstract: I'll describe recent work investigating the arboreal Galoisrepresentation attached to a degree-2 rational function, focusing on the case where the function commuteswith a non-trivial Mobius transformation. In a sense this is a dynamical systems analogue to the p-adic Galois representation attached to an elliptic curve, with particular attention to the CM case. In joint work with Michelle Manes, we give criteria for the image of this representation to be large, and show thatthese criteria are often satisfied in the "CM" case.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jonathan Blackhurst ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Polynomials of the Bifurcation Points of the Logistic Map <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: The logistic map f(r,x)=rx(1-x) was originally studied by ecologists modeling the population of a species from one generation to the next. Here, the population of the next generation f(r,x) depends on the population x of the current generation and a parameter r called the probiotic potential. To find the long-term behavior of the population for a fixed r, we look at iterates of the critical point c=1/2 under the map f. If 0<r<2 the iterates approach zero, so the population goes extinct. If 2<r<3, the iterates approach a single non-zero value, and the population is in equilibrium. If 3<r<1+sqrt(6), the iterates oscillate between two values (even iterates approach one value, while odd iterates approach another) in a boom-and-bust cycle. As r increases, the population begins oscillating between four values, then eight, then sixteen, and this period-doubling continues until an accumulation point (r=3.57, approximately) where the behavior of the population is no longer periodic. Even after the accumulation point, iterates of the critical point may begin again to exhibit periodic behavior. For example, at r=1+sqrt(8), they oscillate between three values. These values of r—2, 3, 1+sqrt(6), and 1+sqrt(8)—where qualitative behavior of the model changes are called bifurcation points. Little has been known about the polynomials these algebraic numbers satisfy. We find their degrees, show that their roots come in pairs whose mean is 1, put constraints on the size and prime factors of their constant coefficients, and record the number of real roots.<br />
|} <br />
</center><br />
<br />
== Liang Xiao ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: There is an analogy among vector bundles with integrable<br />
connections, overconvergent F-isocrystals, and lisse l-adic sheaves.<br />
Given one of the objects, the property of being clean says that the<br />
ramification is controlled by the ramification along all generic<br />
points of the ramified divisors. In this case, one expects that the<br />
Euler characteristics may be expressed in terms of (subsidiary) Swan<br />
conductors; and (in first two cases) the log-characteristic cycles may<br />
be described in terms of refined Swan conductors. I will explain the<br />
proof of this in the vector bundle case and report on the recent<br />
progress on the overconvergent F-isocrystal case if time is permitted.<br />
|} <br />
</center><br />
<br />
== Winnie Li ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1882NTS/Abstracts Spring 20112011-03-25T20:53:20Z<p>Brownda: /* Rafe Jones */</p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Let A be an abelian variety over a number field E, and let v be a finite place of E where A has bad, split, semi-stable reduction. Then the toric part of the reduction of A at v gives rise to a partial integral structure on the (l-adic, p-adic, deRham, log crystalline) cohomology group H^1(A_{E_v} ), arising essentially from the character group of the torus. Let η be a Hodge cycle on A; then one can ask if η is rational (in a precise sense) with respect to this new integral structure on the cohomology. This question was first considered by Andre ́.<br />
Using the theory of Shimura varieties and the Faltings-Chai toroidal compactifications of the moduli of principally polarized abelian varieties, we convert this question into one of deciding if a certain sub-scheme of a torus embedding is again a torus embedding. In the situation where the Mumford-Tate group of A has a reductive model over Zp, for v|p (this is the unramified situation), we employ a generalization of the methods introduced by Faltings and Kisin–initially used to construct smooth integral models of Shimura varieties–to answer this question positively.<br />
A by-product of this rationality result is the construction of good toroidal compactifications of the integral models of Shimura varieties mentioned above. This was in fact the main motivation for considering, in the first place, the possibility of such a result. A formal consequence of the existence of these compactifications is the following result, which is a slightly weakened version of a conjecture of Yasuo Morita: Suppose the Mumford-Tate group G of A is anisotropic mod center, then, for any prime p such that G admits a reductive model over Zp, A has potentially good reduction at all finite places v|p of E.<br />
The first part of the talk will be expository: we will introduce Hodge cycles on abelian varieties and their properties, so that we can state the problem at hand. Then, we will switch track and talk about the question on toric embeddings referenced above. After this, we will focus on the case where the reduction of A at v is a split torus. In this case, the theory is more combinatorial, but the key ideas for the general case are already visible. We will quickly sketch the properties that we need of Shimura varieties and the Faltings-Chai compactification, and see how they can be used to reduce the problem to the one about toric embeddings. If time remains, we will say something about how to solve this latter problem using the Faltings-Kisin method.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== Tony Várilly-Alvarado ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Wei Ho ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rob Rhoades ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Chris Davis ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bianca Viray ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Frank Thorne ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rafe Jones ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Galois theory of iterated quadratic rational functions <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: <br />
Abstract: I'll describe recent work investigating the arboreal Galoisrepresentation attached to a degree-2 rational function, focusing on the case where the function commuteswith a non-trivial Mobius transformation. In a sense this is a dynamical systems analogue to the p-adic Galois representation attached to an elliptic curve, with particular attention to the CM case. In joint work with Michelle Manes, we give criteria for the image of this representation to be large, and show thatthese criteria are often satisfied in the "CM" case.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jonathan Blackhurst ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Polynomials of the Bifurcation Points of the Logistic Map <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: The logistic map f(r,x)=rx(1-x) was originally studied by ecologists modeling the population of a species from one generation to the next. Here, the population of the next generation f(r,x) depends on the population x of the current generation and a parameter r called the probiotic potential. To find the long-term behavior of the population for a fixed r, we look at iterates of the critical point c=1/2 under the map f. If 0<r<2 the iterates approach zero, so the population goes extinct. If 2<r<3, the iterates approach a single non-zero value, and the population is in equilibrium. If 3<r<1+sqrt(6), the iterates oscillate between two values (even iterates approach one value, while odd iterates approach another) in a boom-and-bust cycle. As r increases, the population begins oscillating between four values, then eight, then sixteen, and this period-doubling continues until an accumulation point (r=3.57, approximately) where the behavior of the population is no longer periodic. Even after the accumulation point, iterates of the critical point may begin again to exhibit periodic behavior. For example, at r=1+sqrt(8), they oscillate between three values. These values of r—2, 3, 1+sqrt(6), and 1+sqrt(8)—where qualitative behavior of the model changes are called bifurcation points. Little has been known about the polynomials these algebraic numbers satisfy. We find their degrees, show that their roots come in pairs whose mean is 1, put constraints on the size and prime factors of their constant coefficients, and record the number of real roots.<br />
|} <br />
</center><br />
<br />
== Liang Xiao ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: There is an analogy among vector bundles with integrable<br />
connections, overconvergent F-isocrystals, and lisse l-adic sheaves.<br />
Given one of the objects, the property of being clean says that the<br />
ramification is controlled by the ramification along all generic<br />
points of the ramified divisors. In this case, one expects that the<br />
Euler characteristics may be expressed in terms of (subsidiary) Swan<br />
conductors; and (in first two cases) the log-characteristic cycles may<br />
be described in terms of refined Swan conductors. I will explain the<br />
proof of this in the vector bundle case and report on the recent<br />
progress on the overconvergent F-isocrystal case if time is permitted.<br />
|} <br />
</center><br />
<br />
== Winnie Li ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1881NTS spring 20112011-03-25T20:52:15Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#David_Brown | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Tony_Várilly-Alvarado | <font color="black"><em>Failure of the Hasse principle for Enriques surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| Shamgar Gurevich<br> UW-Madison <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em> Fast Fourier Transform: Why? and How? </em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>Descent on elliptic surfaces and transcendental Brauer element</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bhargav Bhatt <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>Galois theory of iterated quadratic rational functions</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 5 (Thurs)<br />
| bgcolor="#F0B0B0"| Rami Aizenbud, <br> MIT<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em> Multiplicity One Theorems </em></font>]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=1875NTSGrad2011-03-20T00:48:01Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Graduate Student Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Tuesdays at 2:30pm<br />
*'''Where:''' Van Vleck Hall B105 (or possibly B129)<br />
<br />
<br><br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk. <br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 18 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>Organizational meeting</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 25 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Silas Johnson<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>Introduction to Hodge Structures and the Mumford-Tate group</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Mike Woodbury<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Evan Dummit<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>An introduction to Stark's conjecture</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 15 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Daniel Ross<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 22 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Lalit Jain <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 1 (Tue.)<br />
| bgcolor="#F0B0B0"|<br> Luanlei Zhao<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Intro to Jacob forms</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 8 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Marton Hablicsek<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 15 (Tue.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em></em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 22 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Yueke Hu<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 29 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Rachel Davis<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 5 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Timur Nezhmetdinov<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 12 (Tue.)<br />
| bgcolor="#F0B0B0"| Yongqiang Zhao<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Background talk for Frank Thorne's talk</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 19 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Andrew Bridy<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 26 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Jonathan Blackhurst<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Jonathan_Blackhurst | <font color="black"><em>Polynomials of the Bifurcation Points of the Logistic Map</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
----<br />
The Fall 2010 NTS Grad page has moved [http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2010 here:].<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1874NTS/Abstracts Spring 20112011-03-20T00:46:54Z<p>Brownda: </p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Let A be an abelian variety over a number field E, and let v be a finite place of E where A has bad, split, semi-stable reduction. Then the toric part of the reduction of A at v gives rise to a partial integral structure on the (l-adic, p-adic, deRham, log crystalline) cohomology group H^1(A_{E_v} ), arising essentially from the character group of the torus. Let η be a Hodge cycle on A; then one can ask if η is rational (in a precise sense) with respect to this new integral structure on the cohomology. This question was first considered by Andre ́.<br />
Using the theory of Shimura varieties and the Faltings-Chai toroidal compactifications of the moduli of principally polarized abelian varieties, we convert this question into one of deciding if a certain sub-scheme of a torus embedding is again a torus embedding. In the situation where the Mumford-Tate group of A has a reductive model over Zp, for v|p (this is the unramified situation), we employ a generalization of the methods introduced by Faltings and Kisin–initially used to construct smooth integral models of Shimura varieties–to answer this question positively.<br />
A by-product of this rationality result is the construction of good toroidal compactifications of the integral models of Shimura varieties mentioned above. This was in fact the main motivation for considering, in the first place, the possibility of such a result. A formal consequence of the existence of these compactifications is the following result, which is a slightly weakened version of a conjecture of Yasuo Morita: Suppose the Mumford-Tate group G of A is anisotropic mod center, then, for any prime p such that G admits a reductive model over Zp, A has potentially good reduction at all finite places v|p of E.<br />
The first part of the talk will be expository: we will introduce Hodge cycles on abelian varieties and their properties, so that we can state the problem at hand. Then, we will switch track and talk about the question on toric embeddings referenced above. After this, we will focus on the case where the reduction of A at v is a split torus. In this case, the theory is more combinatorial, but the key ideas for the general case are already visible. We will quickly sketch the properties that we need of Shimura varieties and the Faltings-Chai compactification, and see how they can be used to reduce the problem to the one about toric embeddings. If time remains, we will say something about how to solve this latter problem using the Faltings-Kisin method.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== Tony Várilly-Alvarado ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Wei Ho ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rob Rhoades ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Chris Davis ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bianca Viray ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Frank Thorne ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rafe Jones ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jonathan Blackhurst ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Polynomials of the Bifurcation Points of the Logistic Map <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: The logistic map f(r,x)=rx(1-x) was originally studied by ecologists modeling the population of a species from one generation to the next. Here, the population of the next generation f(r,x) depends on the population x of the current generation and a parameter r called the probiotic potential. To find the long-term behavior of the population for a fixed r, we look at iterates of the critical point c=1/2 under the map f. If 0<r<2 the iterates approach zero, so the population goes extinct. If 2<r<3, the iterates approach a single non-zero value, and the population is in equilibrium. If 3<r<1+sqrt(6), the iterates oscillate between two values (even iterates approach one value, while odd iterates approach another) in a boom-and-bust cycle. As r increases, the population begins oscillating between four values, then eight, then sixteen, and this period-doubling continues until an accumulation point (r=3.57, approximately) where the behavior of the population is no longer periodic. Even after the accumulation point, iterates of the critical point may begin again to exhibit periodic behavior. For example, at r=1+sqrt(8), they oscillate between three values. These values of r—2, 3, 1+sqrt(6), and 1+sqrt(8)—where qualitative behavior of the model changes are called bifurcation points. Little has been known about the polynomials these algebraic numbers satisfy. We find their degrees, show that their roots come in pairs whose mean is 1, put constraints on the size and prime factors of their constant coefficients, and record the number of real roots.<br />
|} <br />
</center><br />
<br />
== Liang Xiao ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: There is an analogy among vector bundles with integrable<br />
connections, overconvergent F-isocrystals, and lisse l-adic sheaves.<br />
Given one of the objects, the property of being clean says that the<br />
ramification is controlled by the ramification along all generic<br />
points of the ramified divisors. In this case, one expects that the<br />
Euler characteristics may be expressed in terms of (subsidiary) Swan<br />
conductors; and (in first two cases) the log-characteristic cycles may<br />
be described in terms of refined Swan conductors. I will explain the<br />
proof of this in the vector bundle case and report on the recent<br />
progress on the overconvergent F-isocrystal case if time is permitted.<br />
|} <br />
</center><br />
<br />
== Winnie Li ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=1873NTSGrad2011-03-20T00:45:26Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Graduate Student Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Tuesdays at 2:30pm<br />
*'''Where:''' Van Vleck Hall B105 (or possibly B129)<br />
<br />
<br><br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk. <br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 18 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>Organizational meeting</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 25 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Silas Johnson<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>Introduction to Hodge Structures and the Mumford-Tate group</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Mike Woodbury<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Evan Dummit<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>An introduction to Stark's conjecture</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 15 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Daniel Ross<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 22 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Lalit Jain <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 1 (Tue.)<br />
| bgcolor="#F0B0B0"|<br> Luanlei Zhao<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Intro to Jacob forms</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 8 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Marton Hablicsek<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 15 (Tue.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em></em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 22 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Yueke Hu<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 29 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Rachel Davis<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 5 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Timur Nezhmetdinov<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 12 (Tue.)<br />
| bgcolor="#F0B0B0"| Yongqiang Zhao<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Background talk for Frank Thorne's talk</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 19 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Andrew Bridy<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 26 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Jonathan Blackhurst<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Polynomials of the Bifurcation Points of the Logistic Map</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
----<br />
The Fall 2010 NTS Grad page has moved [http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2010 here:].<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=Algebraic_Geometry_Seminar_Spring_2011&diff=1800Algebraic Geometry Seminar Spring 20112011-02-25T01:09:18Z<p>Brownda: /* Spring 2011 */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B305.<br />
<br />
The schedule for the previous semester is [https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar_Fall_2010 here].<br />
<br />
== Spring 2011 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan. 21<br />
|Anton Geraschenko (UC Berkeley)<br />
|''Toric Artin Stacks''<br />
|David Brown<br />
|-<br />
|Jan. 28<br />
|Anatoly Libgober (UIC)<br />
|''Mordell Weil groups of iso-trivial abelian varieties and Alexander polynomials''<br />
|Laurentiu Maxim<br />
|-<br />
|Feb. 4<br />
|Valery Lunts (Indiana-Bloomington)<br />
|''Lefschetz fixed point theorems for algebraic varieties and DG algebras''<br />
|Andrei Caldararu<br />
|-<br />
|Feb. 18<br />
|Tony Várilly-Alvarado (Rice)<br />
|''Transcendental obstructions to weak approximation on general K3 surfaces''<br />
|David Brown<br />
|-<br />
|Mar. 4<br />
|Si Li (Harvard)<br />
|''Higher Genus Mirror Symmetry''<br />
|Junwu Tu<br />
|-<br />
|Mar. 25<br />
|Srikanth Iyengar (Nebraska)<br />
|''TBA''<br />
|Andrei Caldararu<br />
|-<br />
|April 8<br />
|Greg Pearlstein (Michigan State)<br />
|''TBA''<br />
|Laurentiu Maxim<br />
|-<br />
|Apr. 15<br />
|Orit Davidovich (UT-Austin)<br />
|''TBA''<br />
|Andrei Caldararu<br />
|-<br />
|May 6<br />
|Hal Schenck (UIUC)<br />
|''TBA''<br />
|Andrei Caldararu<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Anton Geraschenko''' ''Toric Artin Stacks''<br />
<br />
Toric varieties provide a fantastic testing ground for ideas about varieties. Their main feature is that geometric properties of toric varieties correspond to combinatorial properties of their fans. In this talk, I'll briefly review some facts about toric varieties, then define a notion of a stacky fan and the toric Artin stack associated to a stacky fan. I'll state and prove some results relating the combinatorics of the fan to the geometry of the stack and show some illustrative examples. If time permits, I'll motivate this notion of toric Artin stacks a bit more by discussing how toric Artin stacks defined by fans compare to possible intrinsic definitions of toric Artin stacks. Some experience with toric varieties or stacks is a plus, but not essential.<br />
<br />
'''Anatoly Libgober''' ''Mordell Weil groups of iso-trivial abelian varieties and Alexander polynomials''<br />
<br />
I will discuss a relation between the Mordell-Weil groups of isotrivial abelian varieties<br />
over function fields of cyclic coverings of projective plane and the Alexander polynomial of the<br />
complement to ramification locus of the latter. The results are based on joint work<br />
with J.I.Cogolludo on families of elliptic curves.<br />
<br />
'''Valery Lunts''' ''Lefschetz fixed point theorems for algebraic varieties and DG algebras''<br />
<br />
I will report on my work in progress about a version of Lefschetz fixed point theorem for <br />
morphisms (more generally for Fourier-Mukai transforms) of smooth projective varieties. There is also <br />
a parallel version for smooth and proper DG algebras.<br />
<br />
'''Si Li''' ''Higher genus mirror symmetry''<br />
<br />
I'll discuss my joint work with Kevin Costello on the geometric<br />
framework of constructing higher genus B-model from perturbative<br />
renormalization of BCOV theory on Calabi-Yau manifolds.<br />
This is conjectured to be the mirror of higher genus Gromov-Witten theory in<br />
the A-model. We carry out the construction in the one-dim cases, i.e.,<br />
elliptic curves, and show that such constructed B-model correlation<br />
functions on the elliptic curve can be identified under the mirror map with<br />
the A-model descendant Gromov-Witten invariants on the mirror. This is the<br />
first compact example where mirror symmetry can<br />
be established at all genera.</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=1799NTSGrad2011-02-25T01:08:16Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Graduate Student Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Tuesdays at 2:30pm<br />
*'''Where:''' Van Vleck Hall B105 (or possibly B129)<br />
<br />
<br><br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk. <br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 18 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>Organizational meeting</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 25 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Silas Johnson<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>Introduction to Hodge Structures and the Mumford-Tate group</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Mike Woodbury<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Evan Dummit<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>An introduction to Stark's conjecture</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 15 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Daniel Ross<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 22 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Lalit Jain <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 1 (Tue.)<br />
| bgcolor="#F0B0B0"|<br> Luanlei Zhao<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Intro to Jacob forms</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 8 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Marton Hablicsek<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 15 (Tue.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em></em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 22 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Yueke Hu<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 29 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Rachel Davis<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 5 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Timur Nezhmetdinov<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 12 (Tue.)<br />
| bgcolor="#F0B0B0"| Yongqiang Zhao<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Background talk for Frank Thorne's talk</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 19 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Andrew Bridy<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 26 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Jonathan Blackhurst<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
----<br />
The Fall 2010 NTS Grad page has moved [http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2010 here:].<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1798NTS spring 20112011-02-25T01:02:20Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#David_Brown | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Tony_Várilly-Alvarado | <font color="black"><em>Failure of the Hasse principle for Enriques surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| Shamgar Gurevich<br> UW-Madison <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em> Canonical Hilbert Space: Why? and How? </em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>Descent on elliptic surfaces and transcendental Brauer element</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bhargav Bhatt <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 5 (Thurs)<br />
| bgcolor="#F0B0B0"| Rami Aizenbud, <br> MIT<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em> Multiplicity One Theorems </em></font>]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1705NTS spring 20112011-02-16T15:46:36Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#David_Brown | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Tony_Várilly-Alvarado | <font color="black"><em>Failure of the Hasse principle for Enriques surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| Shamgar Gurevich<br> UW-Madison <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em> Canonical Hilbert Space: Why? and How? </em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>Descent on elliptic surfaces and transcendental Brauer element</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>Secondary Terms in Counting Functions for Cubic Fields</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 5 (Thurs)<br />
| bgcolor="#F0B0B0"| Rami Aizenbud, <br> MIT<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em> Multiplicity One Theorems </em></font>]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1704NTS spring 20112011-02-16T15:38:12Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#David_Brown | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Tony_Várilly-Alvarado | <font color="black"><em>Failure of the Hasse principle for Enriques surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| Shamgar Gurevich<br> UW-Madison <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em> Canonical Hilbert Space: Why? and How? </em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>Secondary Terms in Counting Functions for Cubic Fields</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 5 (Thurs)<br />
| bgcolor="#F0B0B0"| Rami Aizenbud, <br> MIT<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em> Multiplicity One Theorems </em></font>]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=Algebraic_Geometry_Seminar_Spring_2011&diff=1703Algebraic Geometry Seminar Spring 20112011-02-16T15:37:59Z<p>Brownda: /* Spring 2011 */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B305.<br />
<br />
The schedule for the previous semester is [https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar_Fall_2010 here].<br />
<br />
== Spring 2011 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan. 21<br />
|Anton Geraschenko (UC Berkeley)<br />
|''Toric Artin Stacks''<br />
|David Brown<br />
|-<br />
|Jan. 28<br />
|Anatoly Libgober (UIC)<br />
|''Mordell Weil groups of iso-trivial abelian varieties and Alexander polynomials''<br />
|Laurentiu Maxim<br />
|-<br />
|Feb. 4<br />
|Valery Lunts (Indiana-Bloomington)<br />
|''Lefschetz fixed point theorems for algebraic varieties and DG algebras''<br />
|Andrei Caldararu<br />
|-<br />
|Feb. 18<br />
|Tony Várilly-Alvarado (Rice)<br />
|''Transcendental obstructions to weak approximation on general K3 surfaces''<br />
|David Brown<br />
|-<br />
|Feb. 25<br />
|Bhargav Bhatt (UMich)<br />
|''TBA''<br />
|Jordan Ellenberg<br />
|-<br />
|Mar. 4<br />
|Si Li (Harvard)<br />
|''Higher Genus Mirror Symmetry''<br />
|Junwu Tu<br />
|-<br />
|Mar. 25<br />
|Srikanth Iyengar (Nebraska)<br />
|''TBA''<br />
|Andrei Caldararu<br />
|-<br />
|April 8<br />
|Greg Pearlstein (Michigan State)<br />
|''TBA''<br />
|Laurentiu Maxim<br />
|-<br />
|May 6<br />
|Hal Schenck (UIUC)<br />
|''TBA''<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Anton Geraschenko''' ''Toric Artin Stacks''<br />
<br />
Toric varieties provide a fantastic testing ground for ideas about varieties. Their main feature is that geometric properties of toric varieties correspond to combinatorial properties of their fans. In this talk, I'll briefly review some facts about toric varieties, then define a notion of a stacky fan and the toric Artin stack associated to a stacky fan. I'll state and prove some results relating the combinatorics of the fan to the geometry of the stack and show some illustrative examples. If time permits, I'll motivate this notion of toric Artin stacks a bit more by discussing how toric Artin stacks defined by fans compare to possible intrinsic definitions of toric Artin stacks. Some experience with toric varieties or stacks is a plus, but not essential.<br />
<br />
'''Anatoly Libgober''' ''Mordell Weil groups of iso-trivial abelian varieties and Alexander polynomials''<br />
<br />
I will discuss a relation between the Mordell-Weil groups of isotrivial abelian varieties<br />
over function fields of cyclic coverings of projective plane and the Alexander polynomial of the<br />
complement to ramification locus of the latter. The results are based on joint work<br />
with J.I.Cogolludo on families of elliptic curves.<br />
<br />
'''Valery Lunts''' ''Lefschetz fixed point theorems for algebraic varieties and DG algebras''<br />
<br />
I will report on my work in progress about a version of Lefschetz fixed point theorem for <br />
morphisms (more generally for Fourier-Mukai transforms) of smooth projective varieties. There is also <br />
a parallel version for smooth and proper DG algebras.<br />
<br />
'''Si Li''' ''Higher genus mirror symmetry''<br />
<br />
I'll discuss my joint work with Kevin Costello on the geometric<br />
framework of constructing higher genus B-model from perturbative<br />
renormalization of BCOV theory on Calabi-Yau manifolds.<br />
This is conjectured to be the mirror of higher genus Gromov-Witten theory in<br />
the A-model. We carry out the construction in the one-dim cases, i.e.,<br />
elliptic curves, and show that such constructed B-model correlation<br />
functions on the elliptic curve can be identified under the mirror map with<br />
the A-model descendant Gromov-Witten invariants on the mirror. This is the<br />
first compact example where mirror symmetry can<br />
be established at all genera.</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1654NTS spring 20112011-02-08T22:02:14Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#David_Brown | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Tony_Várilly-Alvarado | <font color="black"><em>Transcendental obstructions to weak approximation on general K3 surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| Shamgar Gurevich<br> UW-Madison <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em> Canonical Hilbert Space: Why? and How? </em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>Secondary Terms in Counting Functions for Cubic Fields</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 5 (Thurs)<br />
| bgcolor="#F0B0B0"| Rami Aizenbud, <br> MIT<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em> Multiplicity One Theorems </em></font>]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1505NTS spring 20112011-01-24T16:04:42Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#David_Brown | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Tony_Várilly-Alvarado | <font color="black"><em>Transcendental obstructions to weak approximation on general K3 surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| Shamgar Gurevich<br> UW-Madison <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>Secondary Terms in Counting Functions for Cubic Fields</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1504NTS spring 20112011-01-24T16:04:18Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#David_Brown | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Tony_Várilly-Alvarado | <font color="black"><em>Transcendental obstructions to weak approximation on general K3 surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| Shamgar Gurevich<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>Secondary Terms in Counting Functions for Cubic Fields</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=Algebraic_Geometry_Seminar_Spring_2011&diff=1486Algebraic Geometry Seminar Spring 20112011-01-21T16:26:56Z<p>Brownda: /* Spring 2011 */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B305.<br />
<br />
The schedule for the previous semester is [https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar_Fall_2010 here].<br />
<br />
== Spring 2011 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan. 21<br />
|Anton Geraschenko (UC Berkeley)<br />
|''Toric Artin Stacks''<br />
|David Brown<br />
|-<br />
|Jan. 28<br />
|Anatoly Libgober (UIC)<br />
|''Mordell Weil groups of iso-trivial abelian varieties and Alexander polynomials''<br />
|Laurentiu Maxim<br />
|-<br />
|Feb. 18<br />
|Tony Várilly-Alvarado (Rice)<br />
|''Failure of the Hasse principle for Enriques surfaces''<br />
|David Brown<br />
|-<br />
|Feb. 25<br />
|Bhargav Bhatt (UMich)<br />
|''TBA''<br />
|Jordan Ellenberg<br />
|-<br />
|Mar. 4<br />
|Si Li (Harvard)<br />
|''Higher Genus Mirror Symmetry''<br />
|Junwu Tu<br />
|-<br />
|Mar. 25<br />
|Srikanth Iyengar (Nebraska)<br />
|''TBA''<br />
|Andrei Caldararu<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Anton Geraschenko''' ''Toric Artin Stacks''<br />
<br />
Toric varieties provide a fantastic testing ground for ideas about varieties. Their main feature is that geometric properties of toric varieties correspond to combinatorial properties of their fans. In this talk, I'll briefly review some facts about toric varieties, then define a notion of a stacky fan and the toric Artin stack associated to a stacky fan. I'll state and prove some results relating the combinatorics of the fan to the geometry of the stack and show some illustrative examples. If time permits, I'll motivate this notion of toric Artin stacks a bit more by discussing how toric Artin stacks defined by fans compare to possible intrinsic definitions of toric Artin stacks. Some experience with toric varieties or stacks is a plus, but not essential.<br />
<br />
'''Anatoly Libgober''' ''Mordell Weil groups of iso-trivial abelian varieties and Alexander polynomials.''<br />
<br />
I will discuss a relation between the Mordell-Weil groups of isotrivial abelian varieties<br />
over function fields of cyclic coverings of projective plane and the Alexander polynomial of the<br />
complement to ramification locus of the latter. The results are based on joint work<br />
with J.I.Cogolludo on families of elliptic curves.</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1485NTS spring 20112011-01-21T16:25:58Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#David_Brown | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Tony_Várilly-Alvarado | <font color="black"><em>Transcendental obstructions to weak approximation on general K3 surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>Secondary Terms in Counting Functions for Cubic Fields</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1484NTS spring 20112011-01-21T16:25:17Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Transcendental obstructions to weak approximation on general K3 surfaces</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>Secondary Terms in Counting Functions for Cubic Fields</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1473NTS/Abstracts Spring 20112011-01-20T18:16:11Z<p>Brownda: /* Liang Xiao */</p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Let A be an abelian variety over a number field E, and let v be a finite place of E where A has bad, split, semi-stable reduction. Then the toric part of the reduction of A at v gives rise to a partial integral structure on the (l-adic, p-adic, deRham, log crystalline) cohomology group H^1(A_{E_v} ), arising essentially from the character group of the torus. Let η be a Hodge cycle on A; then one can ask if η is rational (in a precise sense) with respect to this new integral structure on the cohomology. This question was first considered by Andre ́.<br />
Using the theory of Shimura varieties and the Faltings-Chai toroidal compactifications of the moduli of principally polarized abelian varieties, we convert this question into one of deciding if a certain sub-scheme of a torus embedding is again a torus embedding. In the situation where the Mumford-Tate group of A has a reductive model over Zp, for v|p (this is the unramified situation), we employ a generalization of the methods introduced by Faltings and Kisin–initially used to construct smooth integral models of Shimura varieties–to answer this question positively.<br />
A by-product of this rationality result is the construction of good toroidal compactifications of the integral models of Shimura varieties mentioned above. This was in fact the main motivation for considering, in the first place, the possibility of such a result. A formal consequence of the existence of these compactifications is the following result, which is a slightly weakened version of a conjecture of Yasuo Morita: Suppose the Mumford-Tate group G of A is anisotropic mod center, then, for any prime p such that G admits a reductive model over Zp, A has potentially good reduction at all finite places v|p of E.<br />
The first part of the talk will be expository: we will introduce Hodge cycles on abelian varieties and their properties, so that we can state the problem at hand. Then, we will switch track and talk about the question on toric embeddings referenced above. After this, we will focus on the case where the reduction of A at v is a split torus. In this case, the theory is more combinatorial, but the key ideas for the general case are already visible. We will quickly sketch the properties that we need of Shimura varieties and the Faltings-Chai compactification, and see how they can be used to reduce the problem to the one about toric embeddings. If time remains, we will say something about how to solve this latter problem using the Faltings-Kisin method.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== Tony Várilly-Alvarado ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Wei Ho ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rob Rhoades ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Chris Davis ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bianca Viray ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Frank Thorne ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rafe Jones ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Liang Xiao ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: There is an analogy among vector bundles with integrable<br />
connections, overconvergent F-isocrystals, and lisse l-adic sheaves.<br />
Given one of the objects, the property of being clean says that the<br />
ramification is controlled by the ramification along all generic<br />
points of the ramified divisors. In this case, one expects that the<br />
Euler characteristics may be expressed in terms of (subsidiary) Swan<br />
conductors; and (in first two cases) the log-characteristic cycles may<br />
be described in terms of refined Swan conductors. I will explain the<br />
proof of this in the vector bundle case and report on the recent<br />
progress on the overconvergent F-isocrystal case if time is permitted.<br />
|} <br />
</center><br />
<br />
== Winnie Li ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1472NTS spring 20112011-01-20T18:15:50Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>Secondary Terms in Counting Functions for Cubic Fields</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>Computing log-characteristic cycles using ramification theory</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1464NTS spring 20112011-01-20T00:46:36Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em> Coregular representations and elliptic curves</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>Secondary Terms in Counting Functions for Cubic Fields</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1459NTS spring 20112011-01-19T15:37:32Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>The Overconvergent de Rham-Witt Complex</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>Secondary Terms in Counting Functions for Cubic Fields</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=1448NTSGrad2011-01-18T18:36:12Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Graduate Student Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Tuesdays at 2:30pm<br />
*'''Where:''' Van Vleck Hall B105 (or possibly B129)<br />
<br />
<br><br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk. <br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 18 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>Organizational meeting</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 25 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Silas Johnson<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>Introduction to Hodge Structures and the Mumford-Tate group</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts# | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> Evan Dummit<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>An introduction to Stark's conjecture</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 15 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 22 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 5 (Tue.)<br />
| bgcolor="#F0B0B0"|<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 8 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 15 (Tue.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 22 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 29 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 5 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 12 (Tue.)<br />
| bgcolor="#F0B0B0"| Yongqiang Zhao<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Background talk for Frank Thorne's talk</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 19 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Tue.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
----<br />
The Fall 2010 NTS Grad page has moved [http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2010 here:].<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1440NTS spring 20112011-01-18T05:51:10Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Wei_Ho | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rob_Rhoades | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Chris_Davis | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Andrew_Obus | <font color="black"><em>Cyclic Extensions and the Local Lifting Problem</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bianca_Viray | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Frank_Thorne | <font color="black"><em>SECONDARY TERMS IN COUNTING FUNCTIONS FOR CUBIC FIELDS</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Rafe_Jones | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Liang_Xiao | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Winnie_Li | <font color="black"><em>TBA</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1439NTS/Abstracts Spring 20112011-01-18T05:50:52Z<p>Brownda: </p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== Tony Várilly-Alvarado ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Wei Ho ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rob Rhoades ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Chris Davis ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bianca Viray ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Frank Thorne ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rafe Jones ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Liang Xiao ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
== Winnie Li ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1438NTS/Abstracts Spring 20112011-01-18T05:44:35Z<p>Brownda: </p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== Tony Várilly-Alvarado ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Wei Ho ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Rob Rhoades ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Chris Davis ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bianca Viray ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1437NTS/Abstracts Spring 20112011-01-18T05:40:54Z<p>Brownda: /* TBA */</p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bianca Viray ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1436NTS/Abstracts Spring 20112011-01-18T05:40:40Z<p>Brownda: /* TBA */</p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== Andrew Obus ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Cyclic Extensions and the Local Lifting Problem <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1435NTS/Abstracts Spring 20112011-01-18T05:36:10Z<p>Brownda: </p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: TBA <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1434NTS/Abstracts Spring 20112011-01-18T05:33:25Z<p>Brownda: </p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== David Brown ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
== TBA ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Explicit modular approaches to generalized Fermat equations <br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1433NTS/Abstracts Spring 20112011-01-18T05:30:45Z<p>Brownda: </p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Modular symbol is used to construct p-adic L-functions<br />
associated to a modular form. In this talk, I will explain how to<br />
generalize this powerful tool to the construction of p-adic L-functions<br />
attached to an automorphic representation on GL_{2}(A) where A is the ring<br />
of adeles over a number field. This is a joint work with Matthew Emerton.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
<br />
== David Brown ==<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS_spring_2011&diff=1432NTS spring 20112011-01-18T05:28:35Z<p>Brownda: /* Spring 2011 Semester */</p>
<hr />
<div>= Number Theory Seminar, University of Wisconsin-Madison =<br />
<br />
<br />
*'''When:''' Thursdays at 2:30pm, with the exception of May 2, which is on Monday at 4pm (see below).<br />
*'''Where:''' Van Vleck Hall B129 <br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NTS mailing list:]. <br />
<br />
<br />
<br />
<br />
<br><br />
<br />
<br />
<br />
== Spring 2011 Semester ==<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20 (Thurs.)<br />
| bgcolor="#F0B0B0"| Anton Geraschenko <br> (UC Berkeley)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Anton_Gershaschenko | <font color="black"><em>Moduli of Representations of Unipotent Groups</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Keerthi Madapusi <br> (University of Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Keerthi_Madapusi | <font color="black"><em>A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic<br />
compactifications of Shimura varieties</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Bei Zhang <br> (Northwestern University)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts#Bei_Zhang | <font color="black"><em>p-adic L-function of automorphic form of GL(2)</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> David Brown <br> UW-Madison<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>Explicit modular approaches to generalized Fermat equations</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| Tony Várilly-Alvarado <br>Rice <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Wei Ho<br> Columbia <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 3 (Thurs.)<br />
| bgcolor="#F0B0B0"|Rob Rhoades <br> Stanford<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 10 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 17 (Thurs.)<br />
| bgcolor="#F0B0B0"| No seminar (spring break)<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 24 (Thurs.)<br />
| bgcolor="#F0B0B0"| Chris Davis<br> UC Irvine<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 31 (Thurs.)<br />
| bgcolor="#F0B0B0"| Andrew Obus<br> Columbia<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 7 (Thurs.)<br />
| bgcolor="#F0B0B0"| Bianca Viray<br> Brown <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 14 (Thurs.)<br />
| bgcolor="#F0B0B0"| Frank Thorne <br> (Stanford) <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>SECONDARY TERMS IN COUNTING FUNCTIONS FOR CUBIC FIELDS</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 21 (Thurs.)<br />
| bgcolor="#F0B0B0"| Rafe Jones<br> <br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 28 (Thurs.)<br />
| bgcolor="#F0B0B0"| <br> Liang Xiao (U. Chicago)<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2 (Monday, 4pm)<br />
| bgcolor="#F0B0B0"| Winnie Li, <br> Penn State U and NCTS<br />
| bgcolor="#BCE2FE"|[[NTS/Abstracts | <font color="black"><em>TBA</em></font>]]<br />
|}<br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
----<br />
Also of interest is the [http://www.math.wisc.edu/wiki/index.php/NTSGrad Grad student seminar:] which meets on Tuesdays.<br><br />
The Fall 2010 NTS page has moved [http://www.math.wisc.edu/wiki/index.php/NTS_spring_2011 here:].<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Browndahttps://wiki.math.wisc.edu/index.php?title=NTS/Abstracts_Spring_2011&diff=1430NTS/Abstracts Spring 20112011-01-18T05:06:51Z<p>Brownda: </p>
<hr />
<div>== Anton Gershaschenko ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: Moduli of Representations of Unipotent Groups<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: Representations of reductive groups are discretely parameterized, but unipotent groups can have non-trivial families of representations, so it makes sense try to construct and understand a moduli stack (or space) of representations of a given unipotent group. If you restrict to certain kinds of representations, it is possible to actually get your hands on the moduli stack and to construct a moduli space. I'll summarize the few things I know about the general case and then give you a tour of some interesting features that appear in small examples.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Keerthi Madapusi ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: A rationality property of Hodge cycles on abelian varieties, with an application to arithmetic compactifications of Shimura varieties<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Bei Zhang ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#DDDDDD" align="center"| Title: p-adic L-function of automorphic form of GL(2)<br />
|-<br />
| bgcolor="#DDDDDD"| <br />
Abstract: TBA<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
[http://www.math.wisc.edu/~brownda/ David Brown:]<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:]<br />
<br />
<br><br />
<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Brownda